For generations the process of teaching students how to multiply, divide and subtract decimals and fractions, have led to a variety of teaching aids implemented in this process. Pie charts, fragmented items, and pictures are often used to help the student to visualize the segment or segments associated with the numbers. However, heretofore these aids have lacked in instructional value when attempting multiplication, and division. The current process is designed to provide students with hands-on experiences through the manipulation of models that lead to understanding and applying the principals.
The properties of one “1” are involved in renaming numbers in several different ways. Transparent area models allow the students to feel, touch, and conceptualize representations for one being used to make other representations for one whole and fractions.
The process is advantageous with respect to current processes because: (1) It allows the students to find the transparent area models on their sheets with the correct parts shaded, (2) Students can count the total number of parts and the total number of shaded parts in each model, (3) the relationship of the shaded parts to the total number in each model can be named, (4) By intersecting the vertical transparent area model for one whole with horizontal transparent area models for one whole to show examples of fractions and decimals being renamed several different ways.
The method's approach teaches the appropriate names for one whole fractions, decimals, percents, proportions and equations. All of the work that is done with rational numbers is built on the following principals: 1) one has many names, 2) any number multiplied by one is that number, 3) any number divided by one is that number, and 4) there are many ways to represent numbers.